Quorum rules and voting outcomes: evidence from a lab experiment

Transcription

1 Quorum rules and voting outcomes: evidence from a lab experiment Luís Aguiar-Conraria lfaguiar@eeg.uminho.pt NIPE and Economics Department, University of Minho Pedro C. Magalhães pedro.magalhaes@ics.ul.pt Institute of Social Sciences, University of Lisbon Christoph A. Vanberg vanberg@uni-hd.de Faculty of Economics, University of Heidelberg Abstract If you were unlucky enough to come across this paper, please keep in mind that this is a very preliminary version. At this point, we decline any responsibility on the consequences of using the implications of our analysis in the real world. Please do not cite it and do not circulate it around. Of course, any comments are more than welcome. Keywords: Quorum, voting rules, laboratory experiment. JEL Classification: D72, C91, C92 1

2 1. Introduction In most instances of collective decision-making, it cannot be expected that all members who are entitled to participate will always do so. There may even be instances where most members of a legislature, a city council, a club, a board of directors, or even an electorate end up not showing up when decisions are being made. This fact, together with concerns with the legitimacy and the representativeness of decisions, often results in the adoption of quorum rules. Real life examples of such rules can be found in the standing orders of legislatures (Rasch 1995; Squire 2006), corporate bylaws regulating boards of directors or shareholders meetings (Williams 2006), or statutes and constitutional laws regulating local, state, and national referendums and initiatives (Kaufmann et al. 2008). In the simplest example of a binary decision about preserving or changing a particular status quo, quorum rules establish thresholds that, if not fulfilled, will prevent change from taking place even when a majority of participants is in favor of it. One common type of threshold is provided by a participation quorum, imposing that a minimum number or proportion of the entitled members must participate for the decision to be valid. Another type of threshold is provided by an approval quorum, imposing that the majority voting for change must not be below a minimum number or proportion of the entitled members for that change to take place. A number of recent theoretical studies have focused on the consequences of quorum rules as applied to binary decisions in the context of referendums and initiatives. 1 There are good reasons to focus on these cases. Quorum-busting strategies, well known in legislatures for centuries (Williams 2006), have found more or less evident parallels in referendums and initiatives. In both contemporary (as in Italy Uleri 2002; Kaufmann et al. 2008) and historical (as in the Weimar Republic Suksi 1993) cases, supporters of the status quo have arguably demobilized, with the result that, through the application of participation quorum rules, changes approved by participating majorities have failed to take place. Furthermore, quorum rules for referendums and initiatives are very common. Fourteen European Union member-states establish either participation or approval quorum rules for national referendums and initiatives (Venice Commission 2007). In most states of the German Federation, state and municipal referendums are valid only if 1 When these rules are applied to referendums and initiatives, verification of fulfillment of quorum requirements is made after the vote has taken place. Conversely, quorum rules in decision-making bodies are typically applied before the vote takes place (adjourning the meeting and forcing its repetition), with knowledge about quorum fulfillment being obtained before any vote takes place. For a recent paper on these cases, see Flamand and Trompounis (2012). 2

3 an approval quorum is reached. In these examples, the participation quorum ranges from 30% to 75%, with the mode being 50%. The approval quorum ranges from 25%, which is also the mode, to 50%. Some American states, such as Wyoming and Minnesota (approval quorums) or Massachusetts, Mississippi, and Nebraska (turnout quorums) have similar restrictions, and they can also be found in Colombia, Venezuela or Taiwan (Qvortrup 2005; Herrera and Mattozzi 2010). However, theoretical findings about the consequences of quorum rules are not entirely conclusive. One of the issues addressed by this literature concerns the consequences of participation quorums. Côrte-Real and Pereira (2004) investigate the extent to which outcomes under different rules are consistent with the whole electorate revealing their true preferences through voting. One corollary of their results is that participation quorums creates conditions for a no-show paradox, through which supporters of the status quo may have the possibility to manipulate outcomes by abstaining. Herrera and Mattozzi (2010), in the context of a group turnout model, show that participation quorum requirements, by affecting political parties and interest groups behavior, distort the incentives to mobilize the electorate, do not necessarily favor the status quo, and may reduce turnout to a point where the expected turnout only exceeds the threshold if the requirement is not imposed in the first place. Similarly, Hizen and Shinmyo (2011) find that participation quorums create incentives for strategic abstention when the participation quorum is anything other than negligibly low. A second issue concerns the consequences of participation quorums as compared to those of approval quorums. Herrera and Mattozzi (2006) argue that their analysis of participation quorums carries over to approval quorums, making them essentially equivalent. Aguiar-Conraria and Magalhães (2010b), in the context of a game theoretical pivotal voter model, obtain different results. They show that although approval quorums may also create incentives for strategic abstention and do not necessarily protect the status quo, they should not always produce the same consequences as participation quorums. Finally, Maniquet and Morelli (2011), using large Poisson voting games (Myerson 2000), conclude the approval quorums dominate participation quorums, in the sense that the former give the incentive for people to vote sincerely while participation quorums promote strategic abstention. Therefore, relative to the participation quorum, the approval quorum simplifies preferences and information aggregation. 3

4 Empirical investigation on the consequences of quorum rules in referendums remains, however, extremely scarce. The only empirical work we are aware of is Aguiar- Conraria and Magalhães (2010a), who, using data for all referendums held in current European Union countries from 1970 until 2007, conclude that the existence of a participation quorum decreased turnout by 14 percentage points, while no effect was observed in the presence of approval quorums. However, this study uses observational data. To the best of our knowledge, quorum rules have never been taken to the lab. This paper addresses the consequences of quorum requirements with the use of experimental data, both in terms of the consequences of quorums for turnout and for the properties of the outcomes favored by those quorums. The literature on laboratory experiments of voting games has been quickly growing (see Palfrey 2009 for a review). Previous papers by Schram and Sonnemans (1996), Morton and Tyran (2011), Battaglini et al. (2010), and Groβer and Schram (2006 and 2010) have provided laboratory evidence on strategic abstention. We base our experiment on the pivotal voter model (Palfrey and Rosenthal 1985), whose implications and comparative static predictions have been supported by observational and experimental evidence (Blais 2000, Levine and Palfrey 2007, Coate et al. 2008, Palfrey 2009). In particular, our experiment resembles most the one by Levine and Palfrey (2007). We modify it in three regards. First, we modify the model to allow for quorum restrictions, allowing for the comparison of voting outcomes with and without quorum rules, across different distributions of supporters. Second, we elicit from participants a cutoff value, forcing them to report their willingness to pay in order to cast a vote. This is motivated by the fact that we are testing the effects of quorum rules in participation, not the use of the cutoff values. Finally, like Börgers (2004) and Coate et al. (2008), the number of people that support each of the two options under vote is uncertain. This extension is useful because with a participation quorum of, say, 50%, if it is known with certainty that supporters only represent 45% of the electorate, the game would became too easy for nayers, who would only need to abstain to ensure victory. We confirm that quorum rules have consequences on turnout. First, on average, quorums decrease participants willingness to pay in order to cast a vote. Second, quorums have different effects conditional on electors preferences: they increase the turnout rate of changers (preference for changing the status quo) and decrease the turnout rate of conservatives (preference preserving the status quo). Third, different 4

5 quorums have different effects depending also on whether changers or conservatives are expected to be in the majority. The participation of changers is enhanced by both types of quorums; however when a changer expects to be in minority the effect is stronger in the presence of a participation quorum. Conservatives are demobilized by both types of quorums, however this effect is much stronger in the case of a participation quorum. In fact, quorums actually increase the probability that conservatives boycott the election (willingness to pay equal to 0), and do so massively (increasing that probability by more than 40 percentage points) in the case of participation quorums. 5

6 2. A pivotal voter model Our support model is the traditional pivotal voter model with aggregate uncertainty (as in Coate el al and Börgers 2004) modified to accommodate different quorum rules see Aguiar-Conraria and Magalhães (2010b). We focus on binary choice problems. Voting Yes corresponds to voting for changing the status quo; and No to preserve it. We will call changers to Yes supporters. Opponents are the conservatives. Each player must decide whether to vote according to his preferences or to abstain. Assume that there are electors ( ) and that each faces a cost of voting given by, where is the realization of a uniformly distributed random variable, [ ], in our experiment. Each voter has perfect knowledge about his/her own costs, but only knows the distribution of the other voters. Also, each elector knows his own type and knows the probability,, that each other individual elector favors the proposal. Given that we have groups of nine students playing the game in the lab, in our theoretical derivations see appendix we will assume that is an odd number. If Yes wins the election, changers obtain a benefit. Conservatives have a benefit of. As Palfrey and Levine, we will consider symmetric benefits: in our experiment we will have. The Yes option wins with if it receives more votes than the No option and if the quorum requirements (if they exist) are satisfied. If the quorum is met and there is a tie in the number of votes, the Yes option wins with 50 per cent probability. 2 A voter derives utility from voting only if he/she is pivotal, i.e. if he/she casts the decisive vote, otherwise, the voter incurred in the cost of voting with no net benefit. The probability of being pivotal depends on the strategies of the other voters. This is a game of incomplete information, with preferences and costs exogenously given. 2 In the case of a tie, we could conceivably consider two options. One, like Palfrey and Levine (2007) is to choose at random, the other would be to favor the status quo. In most real voting situations, there is somebody with the deciding vote, who breaks the tie, like the president of the parliament, the mayor in a city council, the board chair, or the vice president of the United States who presides over the Senate. Ex ante, those situations are similar to a coin flip, unless it is obvious which option that person prefers. Even in that case, the main point remains: the status quo does not always win in case of a tie. There is another reason for us to prefer a coin flip to break the tie: given the small number of students in the lab, favoring the status quo in case of a tie would introduce a strong asymmetry in the game, which would add to the asymmetry caused by the quorum. It is easier to isolate the effect of the quorum if no other asymmetry is introduced in the game. 6

7 In Figure 1, we explain the choices that an elector faces. The mathematical development of the model is left to the appendix. Let the vertical axis represent the percentage of the population that favors the proposal submitted to referendum. In the horizontal axis, we have the percentage of people that oppose the proposal. If there are no quorum requirements (left picture), there is a change in the status quo, with at least 50% probability, if the outcome of the referendum places the results on or above the 45- degree line (meaning that at least 50% of the voters vote Yes ). Therefore, a supporter who believes that the referendum outcome will be placed on the red line believes that he/she will be pivotal. On the other hand, a conservative believes that he/she will be pivotal if he/she believes that the outcome will be on the green line. Figure 1: Pivotal lines The picture in the middle describes a situation where there is an approval quorum of 33%. Therefore, a change the status quo requires the results to be above the 45-degree line and above the 33 percent-yes line. In this case, the Status Quo region increases. There is also a qualitative change on the probability of being pivotal. A supporter may be pivotal if his vote is decisive to reach 50% of the votes (given that the quorum is satisfied) or to reach the quorum (given that at least 50% of the voters choose Yes ). The red line represents these possibilities. For the opponent, the situation is different. A No vote that guarantees a No majority is decisive only if the quorum is met. Therefore, the pivotal green line is reduced, when compared to the first case. Finally, on the right, we describe a situation where there is a participation quorum of 50%. The Change region is reduced to the area above the 50 percent participation rate and above the 45-degree line. A supporter is pivotal if his/her vote is necessary either to reach 50% of the votes (given that the quorum is met) or to meet the quorum (given that the tie is guaranteed). The red line represents this. A conservative may have the decisive vote in two different ways. Given that the quorum is satisfied, then a conservative is 7

8 pivotal, in a good way, if his/her vote guarantees the majority (green line). On the other hand, given that Yes receives majority, an opponent is pivotal, in a bad way, if his/her vote is decisive to meet the quorum requirement (blue line). It is pivotal in a bad way, because the vote is decisive to guarantee an undesired outcome. From the pictures, it is clear what the main objective of imposing a quorum requirement is. The idea is to create a bias for the status quo, by enlarging the Status Quo region. This way, it would be more difficult for very active minorities to change the status quo. 8

9 3. Scenarios and hypothesis Given the lab constraints, we fix the number of eligible voters to be consider two toss-up treatments and two landslide treatments:. We will 1. (Landslide) For each player, the probability of being for Change is, therefore, the expected value of the size of each groups is ( ) ( ). 2. (Toss-up) ( ) ( ) 3. (Toss-up) ( ) ( ). 4. (Landslide) ( ) ( ) We have to calibrate the parameter values for and. The value of is irrelevant, we will consider, so that the strategies give us immediate information on the probability of voting. For example, if, that means that a supporter will vote if the costs are less or equal to 55, which is something that occurs with a probability of 55%. We consider that supporters and opponents have equally strong feelings about the issue. Choosing is associated with an expected turnout of almost 85% in the competitive scenarios with no frictions and 75% in the landslide scenarios. These high turnout rates guarantee that we have interesting multiple equilibriums in the presence of quorum restrictions. The participation quorum is 4 and the approval quorum is 3. To find the equilibriums we solve numerically the systems of equations (A1,nq) and (A2.nq), (A1.aq) and (A2.aq), and (A1.pq) and (A2.pq) in the appendix. Existence of solutions is not a problem, but there are no general uniqueness results. However, given that our problem is only two-dimensional and bounded, one can perform a detailed grid search to look for several equilibriums. Only in the case of no quorum, for our parameters, we found unique equilibriums. The willingness to pay/turnout probabilities associated with each of the Nash equilibriums and the expected percentage of right calls 3 associated with each of the above scenarios are described in Table 1. 3 We say there is a right call when the outcome of the election correctly represents the population preferences. E.g., if the majority of the population is for change, then we consider a right call an outcome in each change reaches the majority of the votes and the quorum is satisfied. In case of a tie, we consider that the outcome is one half correct. These percentages were obtained after one million simulations. 9

10 Table 1: Willingness to pay for different quorum rules, group sizes odds and different profiles Conservatives Changers Average Conservatives Changers Average No quorum eq No quorum eq eq eq Participation eq eq Quorum Participation eq eq Approval Quorum With the help of the above table, we are able to make a series of testable hypothesis: H1 In the presence of quorums we should observe several rounds with very low willingness to pay. Therefore, on average, participation rates will be lower in the presence of quorums. H2 In the presence of quorums we should observe several rounds with conservatives displaying low willingness to pay, while changers display a high willingness to pay. Therefore, we will have huge majorities (close to 100% of the voters), which, sometimes, end up losing the election because the quorum is not met, creating an awkward political situation. Note that these two hypotheses should be clearer in the case of an expected landslide majority for change ( conservatives do not show up. ), because all the equilibriums with quorum imply that H3 Sometimes quorums help a minority to impose change, instead of protecting the status quo. eq Quorum eq eq eq eq eq n = 9, probability of being for change 6/9, participation quorum=4, approval quorum=3 Approval Quorum eq eq eq eq n = 9, probability of being for change 5/9, participation quorum=4, approval quorum=3 Conservatives Changers Average Conservatives Changers Average No quorum eq No quorum eq eq eq eq eq Participation Participation eq eq Quorum Quorum eq eq eq eq eq eq eq eq Approval Approval eq eq Quorum Quorum eq eq eq eq n = 9, probability of being for change 4/9, participation quorum=4, n = 9, probability of being for change 3/9, participation quorum=4, approval quorum=3 approval quorum=3 H4 Although the equilibriums found in Table 1 are quite similar, we expect the no show equilibrium to occur more often when there is a participation quorum. Therefore, 10

11 abstention rate should be higher under the participation quorum than with the approval quorum. Hypothesis 4 cannot be seen by reading Table 1. However, by comparing Figure 1(b) with Figure 1(c), it is obvious that conservatives incentives to abstain are different in the two cases. When facing a participation quorum, the incentive to abstain is an active concern. Just by the act of voting, a conservative may be hurting himself by helping change to reach the required quorum. This effect is captured by the blue line in Figure 1(c) and by the negative sign associate with the third element of equation (A2.pq). In the case of an approval quorum, a conservative voting or not has no influence on meeting the quorum: the incentive to abstain is just a consequence of the voting cost. 11

12 4. Experimental design In each treatment, subjects will be interacting in groups of 9. Each subject is independently assigned a preference for or against the status quo option. Options are neutrally labeled ( Team 1 for status quo, Team 2 for change), and the subjects are told that they are randomly assigned to each team. The random numbers are explained using an urn analogy, aided by graphically displaying an urn on the screen. The probabilities of being assigned to these groups are symmetric, commonly known, and vary between periods. Subjects are informed of the quorum rule in effect (e.g. If fewer than [X] votes are cast, option 1 is chosen. ). They are then asked to report their willingness to pay in order to cast a vote for the option corresponding to their team. Voting costs are determined, choices are implemented, and votes are counted according to the rule. The treatment conditions are: Probabilities of being for / against status quo (4 conditions) and quorum rules (3 conditions: no quorum, participation quorum, approval quorum). That s 4x3 = 12 treatment conditions. We test the no quorum versus approval quorum in some sessions, and no quorum and participation quorum in others. For example, in one session where we consider the Approval Quorum treatment, we will play: 4xNQ, 8xAQ, 4xNQ, 8xAQ, 4xNQ, 8xAQ, 4xNQ, 8xAQ. In second session for the same treatment, we will start with the quorum case, followed by the no quorum. When analyzing the data, we always disregard the information related to the first 12 rounds. We use the strategy method in order to elicit a cutoff value. Our method forces participants to use a cutoff strategy, as predicted by theory. Again, this design choice is motivated by the fact that we are testing the effects of the quorum rules on participation, and not in testing the use of cutoff values itself. This is an important difference between our design and Levine and Palfrey (2007). However they find that to a reasonable approximation individuals followed consistent cutpoint rules (2007: 152). Brandts and Charness (2011) present a survey of the literature regarding whether the strategy method leads to different experimental results than the direct-response method. In most of the comparisons, results are similar in both situations. Finally, another important difference between our design and Levine and Palfrey s (2007) is that the team sizes are randomly determined and unknown to subjects. We follow this approach for 2 reasons. First, we feel that aggregate uncertainty is a realistic and potentially important feature of any voting situation. It feels rather unnatural to take 12

13 a vote on something where the numbers of people supporting and opposing it are commonly known. Second, the theoretical models we are testing assume aggregate uncertainty. Although these models are easily modified to consider the case of known group sizes, the interesting comparative statics predictions occur in more reasonable parameter regions when aggregate uncertainty is assumed. 13

14 5. Aggregate results 5.1 No Quorum versus Participation Quorum First, we look at the average willingness do pay (WTP) in the groups that were subjected to the No Quorum and Participation Quorum Treatments. To test for the effects of a quorum, when compared to the situation of no quorum, we rely on the Wilcoxon signed-rank test (we use the ( )function of Matlab). Eight groups were subjected to the No quorum and Participation quorum treatments. For each group we compute a pair of WTP averages, one for each treatment, and compute the Wilcoxon test to test if the averages are statistically different or not. The results can be read in Table 2 Table 2: The Wilcoxon signed-rank test, No quorum vs. Participation quorum Elector type Subsample Average Willingness to Pay No quorum Participation quorum Wilcoxon test (p-value) 1- All All *** 2- Conservatives All *** 3- Changers All ** 4- Conservatives *** In Majority Changers Conservatives In majority *** Changers (landslide) Conservatives In majority *** Changers (tossup) Conservatives *** In minority Changers *** 12- Conservatives In minority *** Changers (landslide) *** 14- Conservatives In minority *** Changers (tossup) ***, **, * = null rejected at 1%, 5% and 10%; NS = null not rejected at 10%. In the first row of the table, we look at the aggregate. The average willingness to pay with no quorum is on average 56.1 and with a participation quorum is The impact of the quorum on the willingness to pay is, therefore, The Wilcoxon test indicates that the difference in the willingness to pay caused by the presence of the participation quorum is statistically significant at 1%. Therefore, our first result is that in the presence of a participation quorum, the average participation rate decreases. Although this result is by itself interesting, according to Table 1 one should expect different behaviors, depending on several other factors. Namely, depending on whether 14

15 the elector is a conservative or a changer and whether the elector expects to be in minority or majority (and also on the expected size of that minority/majority). In rows 2 and 3, we observe the different effects that the participation quorum has, conditional on the elector s preference. 4 We can see that the conservatives participation rate decreases by 35.3 percentage points (pp), the participation rate of changers increases by 6.3pp. The first effect is significant at 1% and the second at 5%. This leads to our second result: in the aggregate, the participation quorum increases the participation rate of changers and decrease the participation of conservatives. This may have two different awkward consequences. First, if the quorum is met, then the quorum rule, design to favor the status quo, actually ends up favoring change. Second, if the quorum is not satisfied, then one can end up in a situation where a huge majority of voters prefer one option (change) but the actual result is the opposite. 5 In rows 4 and 5, we test the treatment effects on the behavior of electors who expect to be in majority e.g. an election where changers in majority, row 5, we have ( ) ( ) ( ). A conservative who expects to be in majority (row 4) will decrease his/her WTP in the presence of a participation quorum by 45.6 pp. This effect is statistically significant at 1%. On the other hand, a changer expecting to be in majority (row 5) will slightly increase the WTP, however this change is not statistically significant. This is our third result: the participation quorum strongly demobilizes conservatives, who are expected to be in majority, but has no such obvious effect on the behavior of changers, when these are in majority. In rows 6 and 7, and 8 and 9, we separated the cases in which it is expected to have a huge and a slight majority. The results are similar, although it is worth noticing that the demobilizing effect the participation quorum has on conservatives in stronger when the election is expected to be more competitive. In rows 10 and 11, we consider the behavior of electors who expect to be in minority. The quorum powerfully demobilizes conservatives and mobilizes changers. Both effects 4 In the case of No quorum the game is absolutely symmetric and, therefore, it does not make sense to talk about being conservative or not. The only relevant distinction is whether the elector expects to be in minority or majority, and whether one should expect a toss-up election or a landslide. 5 This is not a mere theoretical/ experimental curiosity. In a June 2005 a referendum held in Italy, which would have allowed a change in the legislation regulating in vitro fertilization, 90% of the voters wanted to change the law, but given that the participation quorum was not met, the law remained unaltered. 15

16 are statistically highly significant. In rows 11 and 12, and 13 and 14, we look in more detail to the type of expected conservatives majority. The results are broadly similar, except that the mobilizing effect for changers in minority in a tossup election is much smaller.. Fourth result: in an election where changers are expected to be in minority, the participation quorum enhances changers participation. The demobilization effect among conservatives is similar to the previous scenarios. In sum, it is clear that the participation quorum demobilizes conservatives, who face the difficult decision that their vote may be helping Change to reach the quorum. The effect on changers is positive in landslide elections and non-significant in tossup elections. 5.2 No Quorum versus Approval Quorum Now we perform a similar exercise, but we consider the Approval quorum instead. The results are in Table 3. The first impression, when reading these results, is that the effects of the approval quorum are not as dramatic as the effects of the participation quorum, which we saw before. Still the impacts of the approval quorum are statistically significant. Table 3: The Wilcoxon signed-rank test, No quorum vs. Approval quorum Elector type Subsample Average Willingness to Pay No quorum Approval quorum Wilcoxon test (p-value) 1- All All ** 2- Conservatives All *** 3- Changers All ** 4- Conservatives *** In majority Changers *** 6- Conservatives In majority *** Changers (landslide) *** 8- Conservatives In majority *** Changers (tossup) Conservatives * In minority Changers Conservatives In minority * Changers (landslide) Conservatives In minority * Changers (tossup) ***, **, * = null rejected at 1%, 5% and 10%; ns = null not rejected at 10%. Similar to the effects of the participation quorum, we can see in row 1 of Table 3 that the average willingness to pay decreases (although not as strongly) in the presence of the Approval quorum. And, just like before, rows 2 and 3 show a strong negative 16

17 impact on the participation rate of conservatives, and a positive impact on the participation rate of changers. Therefore, our first results, coincide with our first two results in the previous analysis: (1) in the presence of a participation quorum, the average participation rate decreases, and (2) the participation quorum increases the participation rate of changers and decrease the participation of conservatives. When we look at the treatment effects on the electors who expect to be in majority, the results are no longer equal to what we had in the participation quorum case. We have a new result. While it is true that we still observe a demobilizing effect on conservatives, the mobilizing effect on changers is now much stronger, being significant at 1%. In rows 7, we can see that the mobilizing effects among changers occur when they expect the have a huge majority. Finally, in rows 11, 13 and 15, we can also see that the mobilizing effects among changers are not statistically significant when they expect to be in majority, contrary to what happened with the participation quorum. In sum, while in the aggregate, the both quorum effects seem similar, when we look mpre deeply into the data, we observe that they have asymmetric effects. 5.3 Approval Quorum versus Participation Quorum To compare the two different types of quorums, we rely on the Mann-Whitney U test, for independent samples, because in this case we have eight groups that are subject to the Approval quorum treatment and eight other groups that are subject to the Participation quorum treatment. We will use the ( ) function of Matlab). The results are shown in Table 4. When comparing both types of quorums, there are not as many significant results as we had when we compared any of the quorums with the no quorum case. The most salient effect is that under the approval quorum conservatives tend to show up more than under the participation quorum rule. We see that in rows 2 which would be statistically significant only if we had considered a one-tail test 10 and 14, where we can see that this result is stronger when conservatives are in minority. Although not definitive, row 13 suggests that in the presence of an approval quorum the incentives for changers to vote, when facing a landslide majority, are higher than in the presence of a participation quorum. This evidence is not very strong, because at 17

18 conventional levels of statistical significance, these effects are significant only if we consider a one-tail test. Table 4: The Mann-Whitney U test, Participation quorum vs. Approval quorum Elector type Subsample Average Willingness to Pay Participation quorum Approval quorum Mann-Whitney U test (p-value) 1- All All Conservatives All Changers All Conservatives In Majority 5- Changers Conservatives In majority Changers (landslide) Conservatives In majority Changers (tossup) Conservatives ** In minority 11- Changers Conservatives In minority Changers (landslide) Conservatives In minority ** 15- Changers (tossup) ***, **, * = null rejected at 1%, 5% and 10%; NS = null not rejected at 10%. 18

19 6. Another look at the data: regression analysis By relying on non-parametric tests about the median, one may be throwing valuable information away, because hundreds of actions performed by members of a certain group are reduced to a few averages. A different approach is to use all the information on the individual actions by regression analysis. That is what we do next. We estimate a model after controlling for individual fixed effects, washing out any individual and any group effects, and for the round number which is like a like a time trend with each period corresponding to a round in the game. As before, we excluded de first 12 rounds from the analysis. Table 5: Panel Data model of the Willingness to Pay to vote Coefficient Std. Error Wald test c(q)-c(nq)=0 Wald test c(aq)-c(nq)=0 1- No Quorum, landslide minority AQ, conservative, landslide minority ns 3- PQ, conservative, landslide minority *** 4- AQ, changer, landslide minority ns 5- PQ, changer, landslide minority *** 6- No Quorum, tossup minority AQ, conservative, tossup minority *** 8- PQ, conservative, tossup minority *** 9- AQ, changer, tossup minority ns 10- PQ, changer, tossup minority ** 11- No Quorum, tossup majority AQ, conservative, tossup majority *** 13- PQ, conservative, tossup majority *** 14- AQ, changer, tossup majority ns 15- PQ, changer, tossup majority ns 16- No Quorum, landslide majority AQ, conservative, landslide majority *** 18- PQ, conservative, landslide majority *** 19- AQ, changer, landslide majority *** 20- PQ, changer, landslide majority *** 21- Round *** * *** * *** ns *** ns R-squared 0.50 Total observations 5183 PCSE standard errors & covariance (standard errors clustered by individuals) ***, **, * = null rejected at 1%, 5% and 10%; ns = null not rejected at 10%. 19

20 In Table 5, we have the estimation results. As explanatory variables we have the different treatments, the individual fixed effects (not shown) and the time trend (not statistically significant). We distinguish between landslide and tossup majorities and minorities. In the second to the last column, we include the result of Wald test for the equality between the pair of corresponding coefficients between no quorum and the relevant type of quorum. In the last column we perform the same test to compare pairs of corresponding coefficients between participation quorum and approval quorum. The results are compelling. When comparing the quorum treatments with the no quorum treatments, we basically confirm the results from previous sections. The exception is the effect of the participation quorum on changers. The Wilcoxon test suggested that there was some evidence supporting the idea that this quorum could enhance the participation of changers when they were with an overwhelming majority or in minority in a close race. The evidence is now much stronger, as one can see in rows 10 and 20 of Table 5. Comparing the different quorum rules the results are much sharper, now. For example, the demobilizing effect of conservatives is significantly stronger in the case of the participation quorum than in the case of the approval quorum (this difference is always significant at 1%). For changers, the results are not as clear cut. If in minority, the participation quorum coefficient is marginally larger than the approval quorum coefficient. If in majority, coefficients associated with both types of quorums are not statistically different. 6.1 Quorum busting strategies In the literature, when one discusses the effects of quorums, it is almost mandatory to discuss the possibility of boycotts, i.e. electors who decide to abstain with the firm objective of helping the quorum not to be met. In our setup, that basically corresponds to choosing a willingness to pay equal to zero. 20

21 1,600 1,400 1,200 1, Series: WTP12 Sample 1 48 Observations 5183 Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability Figure 2: Distribution of the willingness to pay In Figure 2, it is obvious that the values for WTP of 0 and 100 work as attractors. To describe the impact of the quorums on the probability of boycotting an election is to create a dummy variable, call it boycott, that takes the value 1 if WTP=0 and zero otherwise and then estimate a binary choice model. That is what we do next with the help of a logit model. 6 We also include group dummies, to control for group effects, and a time trend, i.e., the round number. In Table 6, we have our results. As before, the data includes every individual observation, except the data corresponding to the first 12 rounds In the first three columns, we have the typical information: information on the different treatments, the estimated coefficients and standard errors. We convert that information into the probability of boycotting and, in the last column we have the marginal effects. By marginal effects we mean the impact on the probability of changing from a no quorum treatment to a quorum treatment. 7 The impact of the quorum treatment is statistically significant only for conservatives. The existence of an approval quorum increases the likelihood that a conservative boycotts the election by 14.2 (if in minority) and 22.5 (if in majority) percentage points. The impact of the participation quorum is much stronger. In both cases, the probability of boycotting the election increases by more than 50 pp. 6 We considered the possibility of estimating a fixed effects logit model, however more than one thousand observations were dropped, because of individuals who did not show enough variability. Therefore, we limited ourselves to the traditional logit model, using individual clustered standard errors. 7 To compute the probability of boycott and the marginal effects, we plugged the average group coefficient and considered Round=30. 21

22 Table 6: Logit regression of treatment effects on boycotting decisions Coefficient Std. Error Probability of Boycott 1- No Quorum, landslide minority Marginal effects 2- AQ, conservative, landslide minority PQ, conservative, landslide minority *** 4- AQ, changer, landslide minority PQ, changer, landslide minority No Quorum, tossup minority AQ, conservative, tossup minority *** 8- PQ, conservative, tossup minority *** 9- AQ, changer, tossup minority PQ, changer, tossup minority No Quorum, tossup majority AQ, conservative, tossup majority *** 13- PQ, conservative, tossup majority *** 14- AQ, changer, tossup majority PQ, changer, tossup majority No Quorum, landslide majority AQ, conservative, landslide majority *** 18- PQ, conservative, landslide majority *** 19- AQ, changer, landslide majority PQ, changer, landslide majority * 21- Round Pseudo R Total observations 5183 Standard Errors clustered by individuals ***, **, * = null rejected at 1%, 5% and 10%; ns = null not rejected at 10%. 22

23 7. Conclusion Previous theoretical work on the effects of quorum rules in binary elections has generated, on the one hand, a consistent expectation and, on the other hand, lingering questions. The consistent expectation is that participation quorums should depress turnout, particularly by affecting the propensity to vote of those who prefer the option that would stand if the quorum is not fulfilled. Our experimental results confirm that expectation. The participation quorum made conservatives less inclined to vote, and made them much more likely to boycott the election altogether. A finding that was not present in previous studies is that participation quorum may help to increase turnout for those supporting change. This result was clearer when they expected to be in the minority. That effect, however, was too weak to compensate for the overall negative effect of the participation quorum on turnout. An impressive result, which agrees with the predictions of our model, is that the participation quorum increases the probability that conservatives boycott the election by more than 50 percentage points in most of the scenarios and never less than 43 pp. The consequences of approval quorums have been less clear. Are they essentially equivalent to those of participation quorums (Herrera and Mattozzi 2006) or do they produce different effects (Aguiar-Conraria and Magalhães 2010b; Maniquet and Morelli (2011)? Our results present evidence approval quorums are not equivalent to participation quorums. Although, on average, the approval quorum also depressed turnout, it had, in comparison with the participation quorum, different effects. First, the negative effect on conservatives turnout was always sensibly less pronounced under the approval quorum, and although it also increased the probability of outright boycotts, it did to a lesser extent than the participation quorum. Second, there is weaker evidence that the approval quorum increases the participation of changers. Finally, the results point to the substantive political problems engendered by quorums under some conditions. First, although there are many conditions where quorums do indeed seem to protect the status quo, they do so even in cases where a clear majority of voters prefers change. Second, by increasing the turnout of changers, even in conditions when change is expected to be in the minority, they may contribute to victories for change even when such option if minoritarian. In this way, the very argument that quorums protect the status quo does not seem to hold under all conditions. 23

24 References Aguiar-Conraria, L., & Magalhães, P. C. (2010a). Referendum design, quorum rules and turnout. Public Choice, 144(1), Aguiar-Conraria, L., & Magalhães, P. C. (2010b). How quorum rules distort referendum outcomes: Evidence from a pivotal voter model. European Journal of Political Economy, 26(4), Battaglini, M., Morton, R. B., & Palfrey, T. R. (2010). The swing voter's curse in the laboratory. The Review of Economic Studies, 77(1), Börgers, T., Costly voting. American Economic Review 94(1), Brandts, J., & Charness, G. (2011). The strategy versus the direct-response method: a first survey of experimental comparisons. Experimental Economics, 14(3), Coate, S., Conlin, M. & Moro, A. (2008). The performance of pivotal-voter models in small-scale elections: evidence from Texas liquor referenda. Journal of Public Economics 92(3-4), Côrte-Real, P., Pereira, P.T. (2004). The voter who wasn't there: referenda, representation and abstention. Social Choice and Welfare 22(2), Flamand, S., & Troumpounis, O. (2012). Participation quorums in costly meetings. Public Choice. Grosser, J., & Schram, A. (2006). Neighborhood information exchange and voter participation: an experimental study. American Political Science Review, 100(2), Grosser, J., & Schram, A. (2010). Public opinion polls, voter turnout, and welfare: An experimental study. American Journal of Political Science, 54(3), Herrera, H., & Mattozzi, A. (2006). Quorum and turnout in referenda. Available at SSRN: < Herrera, H., Mattozzi, A. (2010). Quorum and turnout in referenda. Journal of the European Economic Association 8(4), Hizen, Y., & Shinmyo, M. (2011). Imposing a turnout threshold in referendums. Public Choice, 148(3), Kaufmann, B., Büchi, R., & Braun, N. (2008). Guidebook to Direct Democracy in Switzerland and Beyond. Initiative & Referendum Institute Europe. Marburg. Levine, D. K., & Palfrey, T. R. (2007). The paradox of voter participation? A laboratory study. American Political Science Review, 101(1),

25 Maniquet, F., & Morelli, M. (2011). Approval quorums dominate participation quorums. Working paper. Morton, R. B., & Tyran, J. R. (2011). Let the experts decide? Asymmetric information, abstention, and coordination in standing committees. Games and Economic Behavior, 72(2), Myerson, R. B. (2000). Large poisson games. Journal of Economic Theory, 94(1), Palfrey, T. R. (2009). Laboratory experiments in political economy. Annual Review of Political Science, 12, Qvortrup, M. (2005). A Comparative Study of Referendums. Manchester University Press, Manchester UK. Rasch, B. E. (1995). Parliamentary Voting Procedures. In Döring, H. (Ed.). Parliaments and majority rule in Western Europe. Frankfurt: Campus. Schram, A., & Sonnemans, J. (1996). Voter turnout as a participation game: an experimental investigation. International Journal of Game Theory, 25(3), Squire, P. (2006). Historical evolution of legislatures in the United States. Annual Review of Political Science, 9, Suksi, M. (1993). Bringing in the People: A Comparison of the Constitutional forms and Practices of the Referendum. Martinus Nijhoff Publishers, Dordrecht. Uleri, P.V. (2002). On referendum voting in Italy: yes, no or non-vote? How Italian parties learned to control referendums. European Journal of Political Research 41(6), Venice Commission, Code of Good Practice on Referendums. Document CDL- AD(2007)008. Available at (2007)008- e.asp. Williams, J. B. (2006). How to Survive a Terrorist Attack: The Constitution's Majority Quorum Requirement and the Continuity of Congress. William & Mary Law Review, 48,

26 Appendix the mathematics of the pivotal voter model Assume that there are electors ( ) and that each faces a cost of voting given by, where is the realization of a uniformly distributed random variable, [ ], in our experiment. Each voter has perfect knowledge about his/her own costs, but only knows the distribution of the other voters. Also, each elector knows his own type and knows the probability,, that each other individual elector favors the proposal. We assume that is an odd number. If Yes wins the election, changers obtain a benefit. Conservatives have a benefit of in our experiment we will have. The Yes option wins with if it receives more votes than the No option and if the quorum requirements (should they exist) are satisfied. If the quorum is met and there is a tie in the number of votes, the Yes option wins with 50 per cent probability. A strategy for elector is a function that specifies if he/she votes or abstains for each possible realization of. We look for symmetric Bayesian-Nash equilibriums. Symmetry implies that all members of a group follow the same strategy. An elector will vote if the voting cost is below some threshold. Let and be those cut-off values for supporters of change and opponents, respectively. The model with no quorum requirements Consider the choices an elector i faces. Assuming that the remaining electors follow their equilibrium strategies, each changer will vote if his/her voting cost is less than, while conservatives will vote if their voting cost is less than. Let ( ) be the probability that, among the individuals, vote Yes and vote No, given their equilibrium strategies, and, and the voting cost distribution. Given our tiebreak rule, a changer will be pivotal in two cases. First: when, among the other electors, the number of Yes votes is equal to the number of No. In this case, the changer s vote is decisive to guarantee victory for the Yes option. Second, when, among the other electors, the number of Yes votes is equal to the number of No votes minus one. In this case, the changer s vote is decisive to guarantee a chance of 50% of victory for the Yes option. Therefore, the expected benefit of voting is [ ( ) ( ) ] 26